When diplomacy has to be conducted by letter, you know that it still has a long way to go. The news that the Americans have been working on a letter to the Iranian government is hardly a surprise, since President Obama has long made it clear that he was minded to make a new start with Tehran. But wanting a new start and getting one are two different things. The last such missive was from the Iranians to the Americans. It was delivered by the Swiss to the Bush administration and offered talks on Iraq, on nuclear matters, and on Iranian links with Hamas and Hezbollah in return for an end to sanctions and the restoration of normal relations. Bush and Cheney tossed it out of the window, refusing to respond, and even chastised the Swiss for passing it on. Obama's letter, assuming it is finalised and delivered, will constitute in effect the positive reply that ought to have been given to the Iranian overtures at that time. But Iranian politics have moved to the right since those days, the Iranian nuclear programme has advanced, and Iran's close support of movements opposing Israel in the Occupied Territories and Lebanon has intensified.

This hardly means that the Iranians will reject an American letter. They will welcome it, with many reservations and conditions. Hardliners in the regime may calculate that it will lead nowhere, and that some real or manufactured crisis will derail any détente. Centrists and liberals will hope that an Iranian-American settlement on some matters will be possible. Pragmatists of various stripes, with the Iranian economy in trouble, will want an easing of the relationship. A few may hope for the "grand bargain" in which every issue separating the two countries is dealt with in one spectacular package. But even on the most optimistic projection, progress is likely to be partial, for a "grand bargain" between Iran and America could only work as part of a "grand bargain" for the whole Middle East. Would Iran end its support for Hamas and Hezbollah, for instance, without those movements being part of settlements between Israelis and Palestinians and in Lebanon? Could Iran accept curbs on its nuclear programme while Israel's nuclear monopoly continues unchallenged and indeed unacknowledged by the United States? Even on Iraq and Afghanistan, where the interests of the two countries overlap, it is far from clear that Washington and Tehran could get much further than agreeing to disagree on many issues.

At the fundamental level of national psychology there is still a huge gap. Even the rhetoric Obama has deployed to indicate his readiness to talk is problematic. Asking Iran to unclench its fist so as to grasp an outstretched American hand suggests that aggression lies on one side and peaceful intentions on the other. But Iranians of all views do not see it like that. President Mahmound Ahmadinejad has lost popularity at home and never enjoyed support among the large Iranian diaspora scattered around the world. But he spoke for the vast majority of Iranians this week when he called for an American apology for its anti-Iranian acts over the years. For Iranians, as the British-Iranian academic Ali Ansari has pointed out, the history of the quarrel with America begins in 1953, when the Americans and British staged the coup which overthrew Muhammad Mossadeq and allowed the Shah to establish the autocratic regime that was only brought to an end by the Iranian revolution a quarter of a century later. It continued with the support America provided Iraq in the Iran-Iraq war, including, as Patrick Tyler recounts in a new book on American policy in the Middle East, US facilitation of chemical weapon strikes against Iranian troops. And its last chapter came under George W Bush, whose administration ignored Iranian efforts at accommodation, insisted on putting Iran's name up in lights as part of the "axis of evil," and, almost to the last minute, harboured thoughts of an aerial assault on their country.

For the Americans, by contrast, history begins with the seizure of the American embassy in 1979, which lives in their memory as essentially an unprovoked act, since few had, or have, much sense of American responsibility for the course of Iranian events. Ahmadinejad's speech was obviously intended to put the US in the position of a supplicant. Obama's line, by implication, sees Iranian antagonism as essentially perplexing. If Iran would just stop putting obstacles in America's way, the US could make life easier for Iran. It certainly isn't that simple. Both sides want concessions without budging from their main positions. And, if they are to make any real progress, they first need to reconcile their conflicting understanding of the past, and, second, arrive at some agreement about what the Middle East should look like in the future.